Fluorescence anisotropy or fluorescence polarization is the phenomenon where the light emitted by a fluorophore has unequal intensities along different axes of polarization. Early pioneers in the field include Aleksander Jablonski, Gregorio Weber,[1] and Andreas Albrecht.[2] The principles of fluorescence polarization and some applications of the method are presented in Lakowicz's book.[3]
The anisotropy (r) of a light source is defined as the ratio of the polarized component to the total intensity (
IT
| r= | Iz-Iy |
| Ix+Iy+Iz |
When the excitation is polarized along the z-axis, emission from the fluorophore is symmetric around the z-axis(Figure). Hence statistically we have
Ix=Iy
Iy=I\perp
Iz=I\parallel
| r= | I\parallel-I\perp | = |
| I\parallel+2I\perp |
| I\parallel-I\perp | |
| IT |
In fluorescence,[4] a molecule absorbs a photon and gets excited to a higher energy state. After a short delay (the average represented as the fluorescence lifetime
\tau
The first concept to understand for anisotropy measurements is the concept of Brownian motion. Although water at room temperature contained in a glass to the eye may look very still, on the molecular level each water molecule has kinetic energy and thus there are many collisions between water molecules in any amount of time. A nanoparticle (yellow dot in the figure) suspended in solution will undergo a random walk due to the summation of these underlying collisions. The rotational correlation time (Φr), the time it takes for the molecule to rotate 1 radian, is dependent on the viscosity (η), temperature (T), Boltzmann constant (kB) and volume (V) of the nanoparticle:[5]
\phir={{ηV}\over{k{B}T}}
The second concept is photoselection by use of a polarized light. When polarized light is applied to a group of randomly oriented fluorophores, most of the excited molecules will be those oriented within a particular range of angles to the applied polarization. If they do not move, the emitted light will also be polarized within a particular range of angles to the applied light.
For single-photon excitation the intrinsic anisotropy r0 has a maximum theoretical value of 0.4 when the excitation and emission dipoles are parallel and a minimum value of -0.2 when the excitation and emission dipoles are perpendicular.
{r0}={2\over5}\left({{{3{{\cos}2}\beta-1}\over2}}\right)
where β is the angle between the excitation and emission dipoles. For steady-state fluorescence measurements it is usually measured by embedding the fluorophore in a frozen polyol.
Taking the idealistic simplest case a subset of dye molecules suspended in solution that have a mono-exponential fluorescence lifetime
\tau
S={IVV
D={IVV
Dividing the difference by the sum gives the anisotropy decay:
r={D\overS}
The grating factor G is an instrumental preference of the emission optics for the horizontal orientation to the vertical orientation. It can be measured by moving the excitation polarizer to the horizontal orientation and comparing the intensities when the emission polarizer is vertically and horizontally polarized respectively.
G is emission wavelength dependent. Note G in literature is defined as the inverse shown.
The degree of decorrelation in the polarization of the incident and emitted light depends on how quickly the fluorophore orientation gets scrambled (the rotational lifetime
\phi
\tau
| r(\tau)= | r0 |
| 1+\tau/\tauc |
Where r is the observed anisotropy, r0 is the intrinsic anisotropy of the molecule,
\tau
\tauc
This analysis is valid only if the fluorophores are relatively far apart. If they are very close to another, they can exchange energy by FRET and because the emission can occur from one of many independently moving (or oriented) molecules this results in a lower than expected anisotropy or a greater decorrelation. This type of homotransfer Förster resonance energy transfer is called energy migration FRET or emFRET.
Steady-state fluorescence anisotropy only give an "average" anisotropy. Much more information can be obtained with time-resolved fluorescence anisotropy[7] where the decay time, residual anisotropy and rotational correlation time can all be determined from fitting the anisotropy decay. Typically a vertically pulsed laser source is used for excitation and timing electronics are added between the start pulses of the laser (start) and the measurement of the fluorescence photons (stop). The technique Time-Correlated Single Photon Counting (TCSPC) is typically employed.
Again using the idealistic simplest case a subset of dye molecules suspended in solution that have a mono-exponential fluorescence lifetime
\tau
\tau
\tau
\tau
S(t)=G{IVV
D(t)=G{IVV
Dividing the difference by the sum gives the anisotropy decay:
r(t)={D(t)\overS(t)}
In the simplest case for only one species of spherical dye:
r(t)={r0}\exp\left({-{t\over{{\phir}}}}\right)
Fluorescence anisotropy can be used to measure the binding constants and kinetics of reactions that cause a change in the rotational time of the molecules. If the fluorophore is a small molecule, the rate at which it tumbles can decrease significantly when it is bound to a large protein. If the fluorophore is attached to the larger protein in a binding pair, the difference in polarization between bound and unbound states will be smaller (because the unbound protein will already be fairly stable and tumble slowly to begin with) and the measurement will be less accurate. The degree of binding is calculated by using the difference in anisotropy of the partially bound, free and fully bound (large excess of protein) states measured by titrating the two binding partners.
If the fluorophore is bound to a relatively large molecule like a protein or an RNA, the change in the mobility accompanying folding can be used to study the dynamics of folding. This provides a measure of the dynamics of how the protein achieves its final, stable 3D shape. In combination with fluorophores which interact via Förster resonance energy transfer(FRET), fluorescence anisotropy can be used to detect the oligomeric state of complex-forming molecules ("How many of the molecules are interacting?").[8]
Fluorescence anisotropy is also applied to microscopy, with use of polarizers in the path of the illuminating light and also before the camera. This can be used to study the local viscosity of the cytosol or membranes, with the latter giving information about the membrane microstructure and the relative concentrations of various lipids. This technique has also been used to detect the binding of molecules to their partners in signaling cascades in response to certain cues.
The phenomenon of emFRET and the associated decrease in anisotropy when close interactions occur between fluorophores has been used to study the aggregation of proteins in response to signaling.